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Insurance and Probability Weighting Functions

By Ali al-Nowaihi and Sanjit Dhami

Abstract

Evidence shows that (i) people overweight low probabilities and underweight high probabilities, but (ii) ignore events of extremely low probability and treat extremely high probability events as certain. Decision models, such as rank dependent utility (RDU) and cumulative prospect theory (CP), use probability weighting functions. Existing probability weighting functions incorporate (i) but not (ii). Our contribution is threefold. First, we show that this would lead people, even in the presence of fixed costs and actuarially unfair premiums, to insure fully against losses of sufficiently low probability. This is contrary to the evidence. Second, we introduce a new class of probability weighting functions, which we call higher order Prelec probability weighting functions, that incorporate (i) and (ii). Third, we show that if RDU or CP are combined with our new probability weighting function, then a decision maker will not buy insurance against a loss of sufficiently low probability; in agreement with the evidence. We also show that our weighting function solves the St. Petersburg paradox that reemerges under RDU and CP

Topics: Decision making under risk, Prelec’s probability weighting function, Higher order Prelec probability weighting functions, Behavioral economics, Rank dependent utility theory, Prospect theory, Insurance, St. Petersburg paradox
Publisher: Dept. of Economics, University of Leicester
Year: 2006
OAI identifier: oai:lra.le.ac.uk:2381/4454

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Citations

  1. (2005). A simple derivation of Prelec’s probability weighting function. doi
  2. (1954). 1738. Exposition of a New Theory of the Measurement of Risk. English translation in Econometrica 22, doi
  3. (2004). Back to the St. Petersburg paradox? CERGE-EI working paper series
  4. (1999). On the shape of the probability weighting function. doi
  5. (1979). Prospect theory : An analysis of decision under risk. doi
  6. (1978). Disaster insurance protection: Public policy lessons,
  7. The influence of probability on risky choice: A parametric investigation. doi
  8. (2001). Reduction invariance and Prelec’s weighting functions. doi
  9. (2005). Cumulative prospect theory and gambling. doi
  10. (1998). The probability weighting function. doi
  11. (1982). A theory of anticipated utility. doi
  12. (1993). Generalized Expected Utility Theory, doi
  13. (2006). Cumulative prospect theory and the St. Petersburg paradox. doi
  14. (1992). Advances in prospect theory : Cumulative representation of uncertainty. doi

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